Multi-objective micro-geometry optimization of planetary gear reducers based on static-dynamic analysis and experimental validation

Abstract

Partial loading and surface wear induced by elastic deformation and machining errors are critical factors causing vibration and noise in planetary gear trains. To mitigate these issues, this paper proposes a multi-objective optimization method for gear tooth modification. Based on a comprehensive analysis of the static and dynamic characteristics of a two-stage planetary gear set, a multi-objective function is established to minimize transmission error, meshing force, unit normal load, and tooth root bending stress. A hybrid optimization strategy, integrating a combined weighting method with a Genetic Algorithm (GA), is employed to determine the optimal micro-geometry parameters. Verification is conducted through static-dynamic simulations and prototype experiments. The results demonstrate that transmission error decreases by 18.91% (from 0.37 to 0.30  $\mu$ m) after optimization. The meshing force decreases from 65.9 to 56.6 N (13.85%), the unit normal load decreases from 95.4 to 83.5 N/mm (12.47%), and the tooth root bending stress decreases from 270.3 to 220.8 MPa (18.30%). In addition, the peak vibration acceleration is reduced from 8.12 to 5.77 m/s² (28.94%), while the noise sound pressure level decreases from 70.2 to 64.8 dB(A) (7.69%). Optimized micro-geometry effectively ameliorates impact shocks during gear engagement and disengagement, thus enhancing transmission efficiency. This study provides a valuable reference for the low-noise design and vibration control of planetary gear reducers.